Experimental Study On The Teaching Of Linear Equation With One Unknown Based On Understanding

Linear equation with one unknown is the core knowledge in the field of algebra,which plays a key role in the transition from arithmetic thinking to algebraic thinking for students.At the same time,it can promote the development of students ' applying ability and mathematical modeling accomplishment by cultivating students who to solve practical problems by using equation model.The development of students 'algebraic thinking requires the study of meaning construction,and the process of meaning construction is the process of understanding,therefore,students 'understanding of algebraic knowledge is helpful to the development of algebraic thinking and applying ability.In this paper,through analyzing the answer of unit test volume about the linear equation with one unknown by text analysis,which from the current second grade students,we get the types of errors that may occur in the process of students learning the linear equation with one unknown.Through interviewing all the mathematics teachers who are currently teaching in the second grade and the students who are representative in the second grade by interview method,we get the reasons for the mistakes from the perspective of teachers and students.Aiming at the types and causes of errors in the process of learning the linear equation with one unknown of first-year students,based on the perspective of understanding,taking constructivist learning theory and learning pyramid principle as the theoretical basis,and under the guidance of the framework of comprehension teaching design,we design the teaching contents of the chapter of Linear equation with one unknown,and select the experimental class and control class to carry out teaching experimental research,which presents two teaching cases of "Solving equations-erase parentheses" and "' Project Hope 'charity performance".At the end of the teaching experiment,we organize the students who are learning in the experimental and control class to participate the unit test of this chapter and to finish the questionnaire of interest in learning the linear equation withone unknown.We analyze the experimental data with horizontal contrast and longitudinal contrast by SAS statistical analysis tool.The experimental results show that:in terms of academic achievement,the average performance of unit tests in the experimental class was 4.3 points higher than that of the control class.The excellent rate of unit test results in experimental class was 3.52% higher than that of control class.The probability of no significant difference in mathematics achievement between the two classes is 0.0177,which shows that the teaching design experiment based on the comprehension teaching design framework can promote the students ' understanding and application of linear equation with one unknown,improve the mathematics learning achievement of students.The difference of mathematics learning's level is significant,which between the experimental class and control class.In terms of interest in learning,the proportion of students in the experimental class who are interested in learning the linear equation with one unknown is 23.07% higher than that of the control class.The probability of no significant difference between students of two classes who are interested in learning the linear equation with one unknown is0.0007,i.e.,the students in the experimental class and control class have a significant difference in their interest in the study of linear equation with one unknown,which shows that the teaching design experiment based on the framework of comprehension teaching design largely improves students ' interest in linear equation with one unknown,stimulates students ' enthusiasm for learning and promotes students ' deep understanding of knowledge.The conclusion of the experimental study:the teaching design based on the framework of comprehension teaching design can promote students' deep understanding of the knowledge method of linear equation with one unknown,and the students' understanding learning activities in the understanding teaching environment can improve students ' learning effect and learning interest.